# TaSIL: Taylor Series Imitation Learning

arXiv: https://arxiv.org/abs/2205.14812 · HTML: https://mlsanity.com/paper/2205.14812/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 17 of its 43 references that are in the map.
- First posted on arXiv 30 May 2022.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 17 of 17)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [DART: Noise Injection for Robust Imitation Learning](https://mlsanity.com/paper/1703.09327/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Knowledge Transfer with Jacobian Matching](https://mlsanity.com/paper/1803.00443/) (2018)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [Learning Stability Certificates from Data](https://mlsanity.com/paper/2008.05952/) (2020)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization](https://mlsanity.com/paper/1907.13122/) (2019)
- [Regret Bounds for Adaptive Nonlinear Control](https://mlsanity.com/paper/2011.13101/) (2020)
- [Learning Contracting Vector Fields For Stable Imitation Learning](https://mlsanity.com/paper/1804.04878/) (2018)

## Built on by (most cited first, 21 of 21)

- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [JUICER: Data-Efficient Imitation Learning for Robotic Assembly](https://mlsanity.com/paper/2404.03729/) (2024)
- [Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior](https://mlsanity.com/paper/2307.14619/) (2023)
- [Multi-Task Imitation Learning for Linear Dynamical Systems](https://mlsanity.com/paper/2212.00186/) (2022)
- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)
- [Butterfly Effects of SGD Noise: Error Amplification in Behavior Cloning and Autoregression](https://mlsanity.com/paper/2310.11428/) (2023)
- [SAFE-GIL: SAFEty Guided Imitation Learning for Robotic Systems](https://mlsanity.com/paper/2404.05249/) (2024)
- [CCIL: Context-conditioned imitation learning for urban driving](https://mlsanity.com/paper/2305.02649/) (2023)
- [Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policies](https://mlsanity.com/paper/2309.01884/) (2023)
- [Model Predictive Control via On-Policy Imitation Learning](https://mlsanity.com/paper/2210.09206/) (2022)
- [Oracle-Efficient Smoothed Online Learning for Piecewise Continuous Decision Making](https://mlsanity.com/paper/2302.05430/) (2023)
- [The Power of Learned Locally Linear Models for Nonlinear Policy Optimization](https://mlsanity.com/paper/2305.09619/) (2023)
- [On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control](https://mlsanity.com/paper/2306.01914/) (2023)
- [A Model-Based Approach to Imitation Learning through Multi-Step Predictions](https://mlsanity.com/paper/2504.13413/) (2025)
- [A Test-Function Approach to Incremental Stability](https://mlsanity.com/paper/2507.00695/) (2025)
- [Safety-Aware Imitation Learning via MPC-Guided Disturbance Injection](https://mlsanity.com/paper/2508.03129/) (2025)
- [Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomy](https://mlsanity.com/paper/2512.17899/) (2025)
- [Accelerating trajectory optimization with Sobolev-trained diffusion policies](https://mlsanity.com/paper/2604.19011/) (2026)
- [Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control](https://mlsanity.com/paper/2410.00859/) (2024)
- [Understanding Behavior Cloning with Action Quantization](https://mlsanity.com/paper/2603.20538/) (2026)
- [Distributionally Robust and Safe Imitation Learning](https://mlsanity.com/paper/2607.13436/) (2026)

## Abstract (arXiv)

We propose Taylor Series Imitation Learning (TaSIL), a simple augmentation to standard behavior cloning losses in the context of continuous control. TaSIL penalizes deviations in the higher-order Taylor series terms between the learned and expert policies. We show that experts satisfying a notion of textitincremental input-to-state stability are easy to learn, in the sense that a small TaSIL-augmented imitation loss over expert trajectories guarantees a small imitation loss over trajectories generated by the learned policy. We provide sample-complexity bounds for TaSIL that scale as tildeO(1/n) in the realizable setting, for n the number of expert demonstrations. Finally, we demonstrate experimentally the relationship between the robustness of the expert policy and the order of Taylor expansion required in TaSIL, and compare standard Behavior Cloning, DART, and DAgger with TaSIL-loss-augmented variants. In all cases, we show significant improvement over baselines across a variety of MuJoCo tasks.